(define \$x (* r (cos θ))) (define \$y (* r (sin θ))) (define \$u-r (∂/∂ (u x y) r)) u-r ;(+ (* (u|1 (* r (cos θ)) (* r (sin θ))) (cos θ)) ; (* (u|2 (* r (cos θ)) (* r (sin θ))) (sin θ))) (define \$u-r-r (∂/∂ (∂/∂ (u x y) r) r)) u-r-r ;(+ (* (u|1|1 (* r (cos θ)) (* r (sin θ))) (cos θ)^2) ; (* (u|1|2 (* r (cos θ)) (* r (sin θ))) (sin θ) (cos θ)) ; (* (u|2|1 (* r (cos θ)) (* r (sin θ))) (cos θ) (sin θ)) ; (* (u|2|2 (* r (cos θ)) (* r (sin θ))) (sin θ)^2)) (define \$u-θ (∂/∂ (u x y) θ)) u-θ ;(+ (* -1 (u|1 (* r (cos θ)) (* r (sin θ))) r (sin θ)) ; (* (u|2 (* r (cos θ)) (* r (sin θ))) r (cos θ))) (define \$u-θ-θ (∂/∂ (∂/∂ (u x y) θ) θ)) u-θ-θ ;(+ (* (u|1|1 (* r (cos θ)) (* r (sin θ))) r^2 (sin θ)^2) ; (* -1 (u|1|2 (* r (cos θ)) (* r (sin θ))) r^2 (cos θ) (sin θ)) ; (* -1 (u|1 (* r (cos θ)) (* r (sin θ))) r (cos θ)) ; (* -1 (u|2|1 (* r (cos θ)) (* r (sin θ))) r^2 (sin θ) (cos θ)) ; (* (u|2|2 (* r (cos θ)) (* r (sin θ))) r^2 (cos θ)^2) ; (* -1 (u|2 (* r (cos θ)) (* r (sin θ))) r (sin θ))) (+ u-r-r (* (/ 1 (** r 2)) u-θ-θ)) ;(/ (+ (* -1 (u|1 (* r (cos θ)) (* r (sin θ))) (cos θ)) ; (* -1 (u|2 (* r (cos θ)) (* r (sin θ))) (sin θ)) ; (* (u|1|1 (* r (cos θ)) (* r (sin θ))) r) ; (* (u|2|2 (* r (cos θ)) (* r (sin θ))) r)) ; r) (+ u-r-r (* (/ 1 r) u-r) (* (/ 1 (** r 2)) u-θ-θ)) ;(+ (u|1|1 (* r (cos θ)) (* r (sin θ))) ; (u|2|2 (* r (cos θ)) (* r (sin θ))))